Economy & Energy
Year II - No 7

Olla_de_oro5362.gif (580 bytes)Main Page
Olla_de_oro5362.gif (580 bytes)Efficiency of the Internal Combustion Engine
Olla_de_oro5362.gif (580 bytes)Sales and Fleet of Otto Vehicles in Brazil
Olla_de_oro5362.gif (580 bytes)Energy Sector Highlights in 1997
Olla_de_oro5362.gif (580 bytes)How to Increase the Capital Productivity

Graphic Edition:
Editoração Eletrônic
Friday, 22 April 2005.


Omar Campos Ferreira
omar@ ecen .com
English Version:
Frida Eidelman



Internal combustion engines have been developed pari passu with petroleum extraction and refining technology. The importance of the engine-petroleum pair in the world economic development in the XX century and the growth of environmental problems inherent to its use causes concern about how long it will last. The basic questions are: a) what are the perspectives of petroleum supply? b) up to what point can the engine efficiency be increased? c) how can the advantages of internal combustion engines and the disadvantages of high emission of atmospheric pollutants and carbon dioxide be conciliated?

About the petroleum supply, e&e presented a summary of the most recent projections which converge to 220 billion tons as the best estimate of the "conventional" petroleum original reserve, of which half has been extracted and used. There is also agreement among the specialized entities on the subject about the development of future exploration: until the year 2050 the extraction should be reduced to 20% of the present one. Since the efficiency is presently 32%, it is obvious that further engine development will not be able to compensate for the decline of petroleum extraction, even when the considered limit would be that imposed by the Principle of Energy Conservation. Therefore, both from the economical and environmental angle, the engine efficiency has fundamental importance , since, for a given driving energy demand, greater efficiency implies less fuel consumption and less pollutants emission.


We propose an evaluation that uses the same methodology we used for evaluating petroleum reserves, which has the advantage of giving a coherent treatment for both questions. We were inspired by the Prof. Israel Vargas’ paper ( "A Brazilian Energy Scenario and the Environmental Overview" , CBPF -CS-003/92) and used the same data source ( "Energy and Power", Chauncey Starr, Scientific American, vol 225, 3, 1971),

a graphic describing the evolution of conversion efficiency for driving energy. Since the article also presents data relative to conversion to electric power, we suppose that the author refers, in the first case, to internal combustion engine, as vapor turbines are now used almost exclusively in thermo-electric plants. There are other ways for projecting efficiency , for example, a study about the evolution of material technology, but more complicated because they do not contemplate all factors that condition the evolution, such as costs, power density, availability of appropriate fuels, etc. The graphic covers the period from 1880 to 2000, with values extrapolated from 1960 on, but we only used data from this century, in which internal combustion engines effectively penetrated the market and vapor turbines were restricted to power plants.

We understand as well that the data reflect the average efficiency of all engines, without distinguishing Diesel from Otto engines. In the period considered, turbines still had a small presence in industry. The methodology used is the logistic projection , already presented in e&e ( "Futurology: Playing with the Logistic Function" , Omar Campos Ferreira / 1996), The fundamental equations are:

        1 -Volterra-Lotka equation

             2 - deduced from 1

   3 - transformed of 2

The first step to determine the efficiency as a function of time is to verify if the logistic function adapts reasonably to the experimental data. In the present case, the original graphic already suggests the logistic shape, but in order to have a reliable projection it is necessary to estimate the constants of equation (2). The most natural way is to determine first the efficiency’s limit value and the constant (a) of equation (1) by adjusting the calculated ratio of the efficiency evolution, as a function of the efficiency, to the parabola ( this adjustment is more sensitive to deviations than that of a logarithmic function, which attenuates them) The calculation of the efficiency evolution is made from observed values. For each time interval there is a ratio that corresponds to the interval’s medium point, in order to make the adjustment by the least square method. Once the constants are obtained, one can use equation (3) for extrapolation. The observed and calculated data are given in the following table.

Table 1

Year 1902 1907 1912 1918 1923 1929 1935 1947 1958 1967 1975
h 4,0 5,0 7,0 10,0 20,0 28,0
h ´ 0,10 0,18 0,25 0,43 0,47
h ´ajust.* 0,15 0,19 0,25 0,38 0,49
F** -2,56 -2,32 -1,94 -1,52 -0,58 0,007
h ajust. 4,0 5,5 7,0 10,0 20,0 28,1

* h ´ajust..   - adjusted value of the efficiency evolution rate.
** F=

The adjusted function are shown in graphics 1 and 2. Since the initial values of efficiency have larger relative deviations, the parabola does not adjusts well to these values. To remove this inconvenience, one can repeat the procedure but we have not made it because the parameter of interest is the limit efficiency , whose adjusted value to the parabola is 56%.

Graphic 1
Otto Cycle engines efficiency evolution rate, observed and ajusted values.
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Graphic 2
Efficiency evolution on time, observed and ajusted values
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The value found for the limit efficiency is coherent with other data. If we consider one Carnot Cycle between the adiabatic combustion temperature of gasoline (2,300 K) and the admitted working temperature for steel (925 K), the expected efficiency would be 59%. The largest efficiency already attained, in maritime Diesel engine with 90,000 HP is 52%. In Otto Cycle engines, which use C gasoline (with anhydrous alcohol), it reaches 32% and those which use hydrated alcohol reach 38%.On the other hand, if we consider efficiency as an exclusive function of the compression ratio, the hydrated alcohol engine, with compression ratio of 12 l should reach 52.5%. Therefore, one can notice that there still is a considerable margin for engine development, not sufficient to compensate for the petroleum extraction decline but still significant in terms of fuel saving and reduction of CO 2 and atmospheric pollutants emission ( CO, HC, Nox, aldehydes, etc.) The possibility of using the ternary mixture gasoline - alcohol - water, already demonstrated in preliminary experiments, will allow for combining gasoline and alcohol as a transition fuel for future solutions ( including the hydrated alcohol itself), combining the calorific properties of the former with the anti-knocking properties of alcohol and of water. It is probable that the development of internal combustion engine will be oriented by more refined analysis of the respective thermodynamic cycles. Comparing the expected efficiency for Otto Cycle engine, calculated as an exclusive function of the compression ratio, with efficiency measured in engines using the present technology, one can notice a large difference, demonstrating the inadequacy of the model used in analyzing the cycle, based exclusively on the Energy Conservation Principle. The possible refinement, at first sight, would stem from considering the irreversibility of real transformations undergone by the fuel mixture ( Second Law of Thermodynamics).

Among the causes of availability loss of fuel energy are the heat transfer under finite temperature difference and the turbulent flow in the throttled section ( air flow control valve, or butterfly valve, intake and discharge valve). The introduction of water in the engine and its vaporization in the intake collector, where the pressure is smaller than the atmospheric one, cools the mixture permitting to decrease the heat extraction and therefore the irreversibility associated with the external cooling.

One can observe that the analysis made permits to discern leaps in the technology development, as that observed in the forties, with the introduction of tetra-ethyl lead as anti-detonating, which permitted to raise the compression ratio from 5:1, allowed by non-additive gasoline, to 7:1. The results obtained by mixing anhydrous alcohol with gasoline in Brazil show that the anti-knocking   effect would be more properly attributed to the ethyl radical than to lead.

This analysis example serves the purpose of corroborating the generally accepted hypothesis that technological development follows the logistic law, as in this case we have a quantifiable parameter of the state of the technology which is the engine’s thermal efficiency.



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